Engine rating pressure ration computer

ABSTRACT

A computer for determining turbine engine pressure ratio limits during engine operation for several inflight ratings. The computer comprises a circular base with a circular overlay mounted thereon for relative movement. Indicia indicative of static air temperature (SAT), total air temperature (TAT) and altitude are placed at different radii in arcuate form on the circular base with arcuate windows being provided on the overlay to read said indicia to insure the overlay is positioned at a desired position with respect to the circular base. While the windows over the altitude indicia only have an arrowhead selector, the window for SAT and TAT has a scale representing Mach number. Also on the base are two sets, or families, of curves representing Mach numbers. Each set of these curves has been calculated to meet with a mating curve formed on one side of each of two other windows on the overlay which is marked in numbers representing engine pressure ratio. While the circular base and circular overlay of this computer can be hand operated, it is to be understood that they can be turned by other means. An instrument wherein the circular base could be moved by total air temperature (TAT) and the circular overlay could be turned by the speed of an aircraft to read in Mach number is contemplated. A fixed hair line in front of the base and overlay is used to read off the indicated Mach number and the indicated total air temperature. When these are properly lined up on the hair line, the static air temperature (SAT) can be read directly therefrom.

United States Patent Toni [ 1 Jan. 18, 1972 -[22] Filed:

[21] Appl.No.: 21,555

[54] ENGINE RATING PRESSURE RATION COMPUTER [72] Inventor: Anselmo Toni,Wapping, Conn. [73] Assignee: United Aircraft Corporation, EastHartford,Conn.

Mar. 20, 1910 3,528,605 Ransone ..235/78 Primary Examiner-Richard B.Wilkinson Assistant Examiner-Stanley A. Wal

Attorney-Jack N. McCarthy "I cu I I In mnm u'z l [a mcrrmculmrcu 5 sum:rm mm mm 1.30

EPR

mu m can. new cm in m mm on (wool Am in sum 0 (1000) Am Arabian-r mun-ptil now i 1 ABSTRACT A computer for determining turbine engine pressureratio limits during engine operation for several intlight ratings. Thecomputer comprises a circular base with a circular overlay mountedthereon for relative movement. Indicia indicative of static airtemperature (SAT), total air temperature (TAT) and altitude are placedat different radii in arcuate form on the circular base with arcuatewindows being provided on the overlay to read said indicia to insuretheoverlay is positioned at a desired position with respect to the circularbase. While the windows over the altitude indicia only have an arrowheadselector, the window for SAT and TAT has a scale representing Machnumber. Also on the base are two sets, or families, of curvesrepresenting Mach numbers. Each set of these curves has been calculatedto meet with a mating curve formed on one side of each of two otherwindows on the overlay which is marked in numbers representing enginepressure ratio.

While the circular base and circular overlay of this computer can behand operated, it is to be understood that they can be turned by othermeans. An instrument wherein the circular base could be moved by'totalair temperature (TAT) and the circular overlay could be turned by thespeed of an aircraft to read in Mach number is contemplated. A fixedhair line in front of the base and overlay is used to read off theindicated Mach number and the indicated total air temperature. Whenthese are properly lined up on the hair line, the static air temperature(SAT) can be read directly therefrom.

/6 10 Claims, 6 Drawing Figures PATENTEU JANI 81972 SHEET 2 0F 5PATENIEU JAN 1 81972 SHEET 3 [IF 5 1 ENGINE RATING PRESSURE RATIONCOMPUTER BACKGROUND OF THE INVENTION This invention relates to acomputer for indicating the desired engine pressure ratio for a specificinflight rating at a predetermined pressure and temperature. Whilehandoperated computers are not new, such as shown by US. Pat. No.3,220,644, the structural arrangement and arrangement of data and itsuse is novel as does the combinationof the SAT and TAT temperature makeswith the Mach number scale.

SUMMARY OF THE INVENTION A primary object of the present invention is toprovide a hand-operated computer which can be used'in the cockpit of anaircraft to determine the required engine pressure ratio (EPR). Thehand-operated computer is an inexpensive computing means on which tocompute the appropriate rating EPR. Further, the operation of thisdevice is relatively simple and'includes in the positioning of thenumbers built-in factors which need not become a problem to theoperator.

This computer aids in achieving long engine life in that the computeraids the pilot or flight engineer by decreasing his work loadrequirement in maintaining engine operation within inflight ratings asset by an aircraft engine manufacturer.

An object of this invention is to provide means for reading SAT byproper relative positioning of a TAT scale and Mach number scale. Thiscan be continuously read by moving a TAT scale so that the actual TAT iskept aligned with a hair line while moving another Mach number scale sothat the actual Mach number is kept aligned with the same hair line.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a view showing the circularbase member of the computer.

. FIG. 2 is a view of the movable circular overlay member of thecomputer which is adapted to be mounted on said base member with the twomembers being movable relative to each other about their center.

FIG. 3 is a view of the computer assembled with the maximum climb (MCL)altitude setting on 25.

FIG. 4 is a view of the computer showing the circular base member movedwith relation to FIG. 3 so that the SAT pointer is set at 22 C.

FIG. 5 is a front view showing a gauge wherein two circular scales arecoaxially mounted.

FIG. 6 is a side view of the gauge shown in FIG. 5.

DESCRIPTION OF THE PREFERRED EMBODIMENT The hand-operated. computer setforth in the figures comprises two main parts, a circular base member 2having a center opening 4 and a circular overlay member 3 having acenter opening 5. When assembled, a nut and bolt arrangement 7 extendsthrough the openings 4 and 5 to maintain the two members 2 and 3 oncenter and permit them relative movement about said center. 7

As shown in FIG. I, the circular base 2 has five sets of indiciaarranged thereon in arcuate fonn at f ve different radii. Around theouter edge of the base member 2 at the largest radii, an arcuate scale20 is set forth with numbers running from -70 to +60 and, as shown inFIG. 2, these numbers will be read through a window 8 which is locatedadjacent the outer edge of the overlay member 3 between lines 10 and 12.A portion of this window 8 is shaded or colored for viewing at 14between lines 10 and 16 while the remainder 17 between the line 16 andline 12 is clear for viewing. Around the inner edge 18 of the window 8an arrowhead appears pointing atthe line 16 with the marking C. SAT" tothe left thereof. Between the arrowhead and the end of the window 12 anarcuate scale I9 is set forth having numerals which indicate MACH NO."The heading C. TAT" appears to the right of the line 12.

The second arcuate scale on base member 2, which is located justradially inwardlyfrom the outer scale 20 (FIG; I), is scale 22. Thisscale has numbers indicating pressure altitudes in thousands runningfrom 10 to 35 and has one noting of "36 and above. These numbers will beread through an arcuate window 24 on member 3 (FIG. 2).- An arrowheadappears along the outer arc of the arcuate window 24 and is used topoint at one of the numbers on scale 22 to determine the maximum cruise(MCR) rating for thataltitucle in a manner to be hereinafter described.

The third arcuate scale on base member 2, which islocated just radiallyinwardly from the scale. 22, .is scale 28 (FIG. I). This scale hasindicia indicating pressure altitudes in thousands running from SI. (sealevel) to, 35 and has one noting of 36 and above." These numbers will beread through an arcuate window 30 on member 3 (FIG. 2). An arrowheadappears along the inner arc of the arcuate window 30 and is used topoint at one of the indicia on scale 28 to determine the maximum climb(MCL) rating for that altitude in a manner to be hereinafter described.

The fourth arcuate scale on base member 2, which is located justradially inwardly from thescale 28, is scale 34 (FIG. I). This scale issimilar to scale 28. in that it has indicia indicating pressurealtitudes in thousands running from SL to 35 and has one noting of 36and above." These indicia will be read through an arcuate window 36 onmember 3 (FIG. 2). An arrowhead appears along the inner arc of thearcuate window and is used to point at one of the indicia on scale 34 todetermine the maximum continuous (MCT) rating or service evaluationclimb (SE CL) rating for that altitude in a manner to be hereinafterdescribed.

The fifth arcuate scale on base member 2, which is located just radiallyinwardly from the scale 34, is scale 40 (FIG. 1). This scale has numbersindicating pressure altitudes in thousands running from 25 to 35 and hasone noting of 36 and above." .These numbers will be read through anarcuate window 42 on member 3 (FIG. 2). An arrowhead appears along theinner arc of the arcuate window 42 and is used to point at one of thenumbers on scale 22 to determine the service evaluation cruise (SE CR)rating for that altitude in a manner to be hereinafter described.

The circular base 2 has two sets, or families, of curves 50 and 52(FIG. 1) representing Mach numbers with the values running from 0.2 to0.95. The family of curves 50 will be read through a window 56in member3 (FIG. 2) while the family of curves 52 will be read through window 58therein. Each of the windows 56 and 58 are of generally irregularcontour so that the necessary portion of the cooperating family ofcurves can be seen therethrough. One side of each window 56 and 58 ismade a predetermined contour such as 60 and 62, respectively, withappropriate numerical markings thereon so that a specific number willappear where each Mach number line intersects. These numbers indicate aspecific engine pressure ratio setting. The family of curves 50 are usedwhen the Mach number is known and one is trying to find the enginepressure ratio (EPR) necessary for a maximum climb, maximum continuous,service evaluation climb, or service evaluation cruise conditions. Thefamily of curves 52 are used when the Mach number is known and one istrying to find the engine pressure ratio (EPR) necessary for maximumcruise conditions.

Each family of curves are plottedfrom data on rating curves forparticular engines or engine models being used. ln-the event an engineis being certified by the FAA, these rating curves would be availabletherefrom.

Charts are printed on the face of the overlay member 3 to make enginepressure ratio (EPR) corrections. The charts shown are for the JT9D-3engine built by Pratt & Whitney Aircraft and used on the Boeing 747aircraft. One chart provides EPR corrections for altitudes over 36,000feet. A second chart makes EPR corrections related to the amount of airbled from the engine compressors for air conditioning. For example, inthe Boeing 747, three packs, or air-conditioningunits, are used and ifone pack or unit were turned off at 25,000 feet this would pennit anaddition of 0.010 to the EPR reading, if

two packs were turned off, it would permit an addition of 0.020 to theEPR reading. The third chart relates to thermal anti-icing (TAl). Aswith the air conditioning, on the Boeing 747 air can be bled to theengine inlets or to the wing to provide for protection against icing. Ifair is being bled to the inlet of the engines for this purpose, it isnecessary that 0.016 be taken away from the value determined for the EPRsetting. A like amount will be taken off if air is being bled to thewings for anti-icing.

For the specific engine model used, to arrive at the specific familiesof curves used in combination with the altitude settings, the inflightratings were referenced to ICAO Standard Day as follows:

l. the Maximum Continuous (MCT) rating and Service Evaluation Climb (SECL) ratings above 25,000 feet- Standard Day +5 C.,

2. Maximum Climb (MCL) rating, all altitudes: Maximum Continuous (MCT)rating below 25,000 feet-Standard Day +8 C.,

3. Service Evaluation Cruise (SE CR) rating, above 25,000

feet-Standard Day +9.6 C.,

4. Maximum Cruise (MCR) rating, all altitudesStandard Day +8 C.

The inflight ratings of this engine referred to in the last paragraphare defined below:

MCTmaximum thrust that may be used continuously during an emergencysituation at the discretion of the pilot. This rating is used tocertificate an aircraft for an engine-out" situation.

MCLmaximum thrust approved for normal climb.

MGR-maximum thrust approved for cruising.

SE CR and SE CL ratings which are higher than the normal maximum climb(MCL) and maximum cruise (MCR) ratings but not greater thanpredetermined FAA rating.

An example will be set forth showing how this computer can be used toarrive at the proper EPR during maximum climb in accordance with themaximum climb (MCL) rating. In this ex ample, the Mach number of theaircraft is 0.80 and it is at an altitude of 25,000 feet. The StandardDay temperature at 25,000 feet is 34.5 C. Since we are discussing themaximum climb rating, the Standard Day +8 C. would be 26.5 C. For thecomputer to determine the rating EPR either SAT or TAT can be used.

1. First the arrowhead on the inner arc of MCL window 30 is placed onthe indicia 25. This has been done in FIG. 3. When this setting is made,the arrowhead opposite line 16 on window 8 indicates approximately 26.5C. and the TAT reading opposite 0.80 MACH NO indicates approximately +5C.

2. If the actual SAT and TAT is colder than -26.5 C. and +5 C.,respectively, then the required EPR is read in the window 60 where the0.80 curve intersects the contour 60. As seen in FIG. 3, this indicatesa value of approximately 1.35.

3. However, if the actual SAT or the TAT is hotter than -26.5 C. and +5C., respectively, then the members 2 and 3 are relatively moved so thatthe arrowhead on line 16 is placed on the value representing the hotterSAT reading, or the 0.80 MACH NO is placed opposite the hotter TATreading as represented on the computer. This has been done in FIG. 4. Anexample is used where the actual SAT is -22 C. and the TAT is +10 C. Itcan be seen that the arrowhead adjacent line 16 points to -22 C. and theTAT reading opposite the 0.80 MACH NO is approximately +10 C. Now, whenthe reading is made in the window 56, it can be seen that the 0.80 curveintersects the contour 60 at 1.31.

To further clarify the above results it can be said of the examples thatif the actual air at 25,000 feet is colder than Standard Day +8 C. theMCL EPR is 1.35 or if the actualair at 25,000 feet is hotter thanStandard Day +8 C. by

the amount used (-22 C. SAT at 25,000 feet) the MCL EPR is 1.31.

The numbers of arcuate scale 20 and the numbers on arcuate scale 19 weredetennined in the following manner. The total air temperature (TA T) isexpressed as a function of static air temperature (SA T) and Mach number(Mn), as follows:

'y for air equals 1 .4 therefore;

These temperatures must be in absolute terms, that is, if degreescentigrade (C.) are used, 273 must be added to obtain the absolutetemperature of degrees Kelvin (K.). To apply the above relationship to aslide rule-type scale the formula is further expressed in logarithmicterms, as follows:

log (TATin K. log (SATin K. log (1+0.2Mn)

Scale 20, see FIG. 1, is a logarithm scale of K. tempera.- tures but thescale is labeled as C., that is, 26.5 C. is actually the logarithm of(27326.5 C.) or the logarithm of 246.5 K. Arcuate scale 19, see FIG. 2,is a logarithm scale of (1+0.2Mn) and is labeled as Mach number; thatis, 0.80 Mach number is actually the logarithm of (1+0.2Mn or logarithm[1+0.2(0.8) or logarithm 1.128. These scales, l9 and 20, now satisfy theequation:

log (TAT in K.) log (SATin K.) log (l+0.2Mn

Using the example set forth before, the settings of which are shown inFIG. 3, the following is set forth:

log (TAT in K.) log (-26.5 C. 273) +.log [1+0.2

log (TATinK.)=log (246.5K.)+log 1.128)

log (TATin K.)==2.3918+0.0524=2.4442

Looking at FIG. 3, it can be seen that opposite 0.80 Mach number onscale 19 is a reading of +5.1 C. TAT. It can be seen that the TATfor aSATof-26.5C. at 0.80 Mach number is 5.1 C.

The altitude scales 22, 28, 34, 40 of FIG. 1 are arranged so that whenthe corresponding rating arrowheads of windows 24, 30, 36, 42 of FIG. 2are opposite a selected altitude, the SAT arrowhead at the line 16 isopposite the appropriate rating temperature in terms of Standard Daytemperature. For example, in FIG. 3, the MCL rating arrowhead on window30 is opposite 25 ,000 feet. Since the Standard Day temperature for 25,000 feet is 34.5 C. and the MCL rating is based on Standard Day +8 C.,therefore when the MCL rating arrowhead is opposite 25,000 feet, the SATarrowhead must point to the Standard Day temperature +8 C., which forthat altitude would be 34.5 C.+ 8 C. or 26.5 C.

With reference to FIGS. 5 and 6 the gauge shown thereby comprises tworelatively movable discs 2A and 3A. A glass view window 102 is fixed inrelation to the members or discs, 2A and 3A has a hair line 104 placedthereon which is used to read the scales on the movable members. Thescale 119 on disc 3A is identical to the scale 19 on FIG. 2 and thescale 120 on the disc 2A is the same as scale 20 in FIG. 1.

The disc 2A is pivotally mounted about its center on a hollow shaft 122which is fixed thereto at one end. The hollow shaft 1.22 can berotatably mounted by any means desired. The disc 3A is mounted forrotation on a solid shaft 124 which has one end fixed thereto. The shaft124 extends through the hollow shaft 122 and is rotatably mountedtherein. The hollow shaft 122 is rotated by a signal from a TATrecorderwhose output is in a form compatible with the scale 120 (see scale 20for details) so that the actual TAT on scale 20 is aligned with the hairline 104. The solid shaft 124 is rotated by a signal from a Mach numberrecorder 132 whose output is in a form compatible to the scale 119 (seescale 19 for details) so that the actual Mach number on scale 19 isaligned with the hair line 104. Since the indicated total airtemperature and the indicated Mach number can be read along the hairline 104, it can be seen that the static air temperature can be read atany given time from the arrowhead on line 116.

I claim:

1. Means for determining static air temperature from total airtemperature and Mach number, comprising, a base member having firstindicia thereon forming an arcuate scale thereon and an axis located onsaid member at the center of said arc, said first indicia being alogarithm scale of K. temperature with the scale labeled as C. anoverlay member rotatably mounted on the said axis to provide relativemovement between said two members, said overlay member having a firstarcuatewindow through which a portion of the first indicia is seen, saidwindow having an arrowhead along its inner arc,-the window on the leftside of said arrowhead is marked C. static air temperature, on the rightside of said arrowhead second indicia fonn an arcuate scale along theinner arc of the window, said second indicia being a logarithm scale ofl+2Mn with the scale labeled as Mach Number.

2. A combination as set forth in claim 1 wherein said base member hasthird indicia thereon forming an arcuate scale, said third indiciarepresenting altitude, said overlay member having a second arcuatewindow through which a portion of said third indicia is seen, anarrowhead being located on the inner arc of said second arcuate windowwhichjs used to indicate the desired altitude represented by said thirdindicia.

3. A computer for determining an engine pressure ratio limit for aparticular engine rating comprising, a base member having first indiciaforming an arc thereon and an axis located on said member at the centerof said arc, said first indicia representing a first variableenvironmental condition affecting engine performance, said base memberalso having second indicia forming a second arc thereon, said secondindicia representing a second variable environmental condition affectingengine performance, a family of curves being located on said base memberwith each curve representing a different value of an engine fiightcondition, an overlay member rotatably mounted on said axis to providerelative movement between said two members, said overlay member having afirst arcuate window through which a portion of the first indicia isseen, said overlay member having a second arcuate window through whichthe second indicia is seen, said overlay member having a third windowthrough which said family of curves is seen, said third window having aside of predetermined contour so that it intersects the family of curvesin a desired manner, third indicia being located along the side of saidthird window of predetermined contour, said third indicia representingan engine operating parameter.

4. A combination as set forth in claim 3 wherein said first variableenvironmental condition affecting engine performance is temperature.

5. A combination as set forth in claim 3 wherein said second variableenvironmental condition affecting engine performance is altitude.

6. A combination as set forth in claim 3 wherein said engine flightcondition represents Mach Number.

7. A combination as set forth in claim 3 wherein said engine operatingparameter is engine pressure ratio.

8. A combination as set forth in claim 3 wherein said first variableenvironmental condition affecting engine performance is temperature,said second variable environmental condition affecting engineperformance is altitude, said engine flight condition is Mach Number,and said engine operating parameter is engine pressure ratio.

9. A combination as set forth in claim 1 wherein a portion of said firstarcuate window is shaded so that the window has a plurality of distinctviewing areas.

10. A computer for determining an engine pressure ratio limit for aparticular engine rating comprising, a base member having first indiciaforming an arc thereon and an axis located on said member at the centerof said arc, said first indicia representing a first variableenvironmental condition afiecting engine performance, said first indiciabeing a logarithm scale of K. temperature with the scale labeled as C.,said baseplate also having second indicia forming a second arc thereon,said second indicia representing a second variable environmentalcondition affecting engine performance, said second indicia beingaltitude, a family of curves being located on said base member with eachcurve representing a different value of an engine flight condition, saidengine flight condition being Mach Number, an overlay member rotatablymounted on said axis to provide relative movement between said twomembers, said overlay member having a first arcuate window through whicha portion of the first indicia is seen, said first arcuate window havinga portion shaded so that the window has a plurality of distinct viewingareas, said first arcuate window having an arrowhead along its inner arepointing at a line between the regular window and the shaded portion,the window on the left side of said arrowhead is marked C. static airtemperature, on the right side of said arrowhead third indicia form anarcuate scale along the inner arc of the window, said third indiciabeing a logarithm scale of (l+2Mn with the scale labeled as Mach Number,said overlay member having a second arcuate window through which thesecond indicia is seen, said second arcuate window having an arrowheadalong its inner arc, said overlay member having a third window throughwhich a portion of said family of curves is seen, said third windowhaving a side of predetermined contour so that it intersects the familyof curves in a desired manner, fourth indicia being located along theside of said third window of predetermined contour, said fourth indiciarepresenting an engine operating parameter, said engine operatingparameter being engine pressure ratio.

1. Means for determining static air temperature from total airtemperature and Mach number, comprising, a base member having firstindicia thereon forming an arcuate scale thereon and an axis located onsaid member at the center of said arc, said first indicia being alogarithm scale of * K. temperature with the scale labeled as * C. anoverlay member rotatably mounted on the said axis to provide relativemovement between said two members, said overlay member having a Firstarcuate window through which a portion of the first indicia is seen,said window having an arrowhead along its inner arc, the window on theleft side of said arrowhead is marked * C. static air temperature, onthe right side of said arrowhead second indicia form an arcuate scalealong the inner arc of the window, said second indicia being a logarithmscale of (1+2Mn2) with the scale labeled as Mach Number.
 2. Acombination as set forth in claim 1 wherein said base member has thirdindicia thereon forming an arcuate scale, said third indiciarepresenting altitude, said overlay member having a second arcuatewindow through which a portion of said third indicia is seen, anarrowhead being located on the inner arc of said second arcuate windowwhich is used to indicate the desired altitude represented by said thirdindicia.
 3. A computer for determining an engine pressure ratio limitfor a particular engine rating comprising, a base member having firstindicia forming an arc thereon and an axis located on said member at thecenter of said arc, said first indicia representing a first variableenvironmental condition affecting engine performance, said base memberalso having second indicia forming a second arc thereon, said secondindicia representing a second variable environmental condition affectingengine performance, a family of curves being located on said base memberwith each curve representing a different value of an engine flightcondition, an overlay member rotatably mounted on said axis to providerelative movement between said two members, said overlay member having afirst arcuate window through which a portion of the first indicia isseen, said overlay member having a second arcuate window through whichthe second indicia is seen, said overlay member having a third windowthrough which said family of curves is seen, said third window having aside of predetermined contour so that it intersects the family of curvesin a desired manner, third indicia being located along the side of saidthird window of predetermined contour, said third indicia representingan engine operating parameter.
 4. A combination as set forth in claim 3wherein said first variable environmental condition affecting engineperformance is temperature.
 5. A combination as set forth in claim 3wherein said second variable environmental condition affecting engineperformance is altitude.
 6. A combination as set forth in claim 3wherein said engine flight condition represents Mach Number.
 7. Acombination as set forth in claim 3 wherein said engine operatingparameter is engine pressure ratio.
 8. A combination as set forth inclaim 3 wherein said first variable environmental condition affectingengine performance is temperature, said second variable environmentalcondition affecting engine performance is altitude, said engine flightcondition is Mach Number, and said engine operating parameter is enginepressure ratio.
 9. A combination as set forth in claim 1 wherein aportion of said first arcuate window is shaded so that the window has aplurality of distinct viewing areas.
 10. A computer for determining anengine pressure ratio limit for a particular engine rating comprising, abase member having first indicia forming an arc thereon and an axislocated on said member at the center of said arc, said first indiciarepresenting a first variable environmental condition affecting engineperformance, said first indicia being a logarithm scale of * K.temperature with the scale labeled as * C., said baseplate also havingsecond indicia forming a second arc thereon, said second indiciarepresenting a second variable environmental condition affecting engineperformance, said second indicia being altitude, a family of curvesbeing located on said base member with each curve representing adifferent value of an engine flight condition, said engine flightcondition being Mach Number, an overlay member rotataBly mounted on saidaxis to provide relative movement between said two members, said overlaymember having a first arcuate window through which a portion of thefirst indicia is seen, said first arcuate window having a portion shadedso that the window has a plurality of distinct viewing areas, said firstarcuate window having an arrowhead along its inner arc pointing at aline between the regular window and the shaded portion, the window onthe left side of said arrowhead is marked * C. static air temperature,on the right side of said arrowhead third indicia form an arcuate scalealong the inner arc of the window, said third indicia being a logarithmscale of (1+2Mn2) with the scale labeled as Mach Number, said overlaymember having a second arcuate window through which the second indiciais seen, said second arcuate window having an arrowhead along its innerarc, said overlay member having a third window through which a portionof said family of curves is seen, said third window having a side ofpredetermined contour so that it intersects the family of curves in adesired manner, fourth indicia being located along the side of saidthird window of predetermined contour, said fourth indicia representingan engine operating parameter, said engine operating parameter beingengine pressure ratio.